After a $3 million restoration, the collection has been put on display at the Washington-based National Archives. But bowing to demands from Iraq's Shiite Muslim-led government, the United States says it will return the collection next summer. Some of the artifacts date to the 16th century.
A National Archives spokeswoman said the materials, whose removal from Baghdad was agreed in 2003 - when a US-led invasion toppled Saddam and the country lurched into widespread sectarian turmoil - would be going back to Iraq and the decision was made by the US State Department.
Members of Iraq's Jewish community, many of whom fled the country in previous decades, say the materials were forcibly taken from them and should not be returned.
Edwin Shuker, 58, who escaped to Britain with his family from Baghdad in 1971, said he had discovered his long-abandoned school certificate on display as part of the National Archives exhibition.
"This is more than a school certificate - it is the identity we were forced to leave behind," he told Reuters, likening the document's journey and survival to his own.
"I would like to be reassured that my children and future generations will have unrestricted access to this collection."
Cynthia Kaplan Shamash, from the New York-based World Organization of Jews from Iraq, said Iraqi Jews were grateful for the restoration but did not want the archive to go back. "Returning the collection to a Jewish-free Iraq in the current conditions is incomprehensible and unacceptable," she said.
Shuker said, "It is not a sectarian issue. Nothing is safe, no shrine or holy place let alone a site where Jewish artifacts are stored. There is a complete breakdown in safety and security in Iraq now."
Sectarian-motivated bombings and shooting attacks by Shiite and Sunni Muslim militants continue almost daily today.
Ali al-Moussawi, an adviser to Iraqi Prime Minister Nuri al-Maliki, said procedures for the archives' return from the United States were "in full swing."
"They have agreed to hand over these documents to the Iraqi side and currently there is no problem, despite attempts by the Jewish community in America to obstruct this matter," he said.
"The Iraqi government will not accept to give up any part of these documents. This is Iraqi legacy owned by all of the Iraqi people and belongs to all the generations, regardless of religious, ethnic or sectarian affiliations."
Iraqi Jews have mobilized support from members of the US Congress to try to block the return. In a letter signed this month by nearly 50 US lawmakers, Secretary of State John Kerry was urged to enable the return of the items "to their rightful owners or their descendents" instead.
"The government of Iraq has no legitimate claim to these artifacts," the letter said.
Iraq's Jewish community numbered around 150,000 in 1947 and has dwindled to just a handful today. Jewish communities in the Middle East stretch back over 2,500 years but anti-Jewish violence, fanned by Arab nationalism, started to sweep through the region in the early 1940s, gradually driving out most Jews.
Conditions deteriorated for Jews in many Arab countries after the establishment of Israel in 1948 and an Israeli-Arab war in which hundreds of thousands of Palestinians fled or were driven from their homes.
The State Department has said it has made a commitment to return the archive. It has paid for Iraqi archivists to train in Washington to make sure that the pieces are preserved and protected, Brett McGurk, Deputy Assistant Secretary for Iraq and Iran, told a hearing earlier this month.
US authorities are expected to talk to the Iraqi ambassador in Washington about the possibility of longer-term loans in the United States to make sure that people can view the pieces, he added.
"We have heard very loudly and clearly the concerns from the community, we've listened to those. We've taken them to heart. And we'll see what we can do."